Standardized Electric-Field-Resolved Molecular Fingerprinting

Field-resolved infrared spectroscopy (FRS) of impulsively excited molecular vibrations can surpass the sensitivity of conventional time-integrating spectroscopies, owing to a temporal separation of the molecular signal from the noisy excitation. However, the resonant response carrying the molecular signal of interest depends on both the amplitude and phase of the excitation, which can vary over time and across different instruments. To date, this has compromised the accuracy with which FRS measurements could be compared, which is a crucial factor for practical applications. Here, we utilize a data processing procedure that overcomes this shortcoming while preserving the sensitivity of FRS. We validate the approach for aqueous solutions of molecules. The employed approach is compatible with established processing and evaluation methods for the analysis of infrared spectra and can be applied to existing spectra from databases, facilitating the spread of FRS to new molecular analytical applications.

1. How to deal with non-zero baselines 2. Appropriate choice of the spectral region of interest 3. Complex-versus real-valued spectra 4. Effect of the shape of the time-filter 5. Analyzing the magnitude of complex time-domain filtered spectra

How to deal with non-zero-baselines
The proposed filter is essentially a high-pass filter.This means that any DC-component will be removed and therefore will change the DC level of the filtered spectra dramatically (see Figure S1a-d).This is the case, for example, when working with (complex) transmission spectra that are close to 1 for small absorption values.If the baseline is to be preserved, one can evaluate the DC level before applying the TDF and then add it back to the filtered result (Figure S2e-h).For small absorptions, a DC value of 1 can also be assumed and subsequently added after filtering.This feature is used in the analysis of the data provided in this paper.

Appropriate choice of the spectral range
A measured spectrum may not be well defined in the entire calculated spectral range due to limited spectral coverage of the light source, strong sample absorption, or other effects.This often leads to strong noise in these regions, which is often noticeable as a fast, random change between small and large values of the spectrum.If these noisy regions are not excluded before applying the TDF, they can affect and deteriorate the results in the actual region of interest (ROI) due to the non-local nature of TDF (Figure S2a-d).Therefore, it is recommended to set the value outside the ROI to the DC-value of the ROI (Figure S2e-h) or only keep the ROI as input to the TDF.

Fig. S2. Effect of the selected spectral range before applying the time-domain filter. a-d: The considered spectral range also includes wavenumber in which the spectrum could not be calculated correctly due to the limited spectral coverage of the utilized light source. This may lead to artefacts in the filtered spectrum (d). e-h:
This can be avoided by applying a spectral filter before applying the actual time-domain filter.

Complex-valued versus real-valued spectra
Spectra obtained with FRS are naturally complex-valued and the concept of TDF can be directly applied to complex spectra.However, in this work, we chose to implement the TDF in a such a way, that real and imaginary parts of the spectrum are treated independently.This implementation offers more flexibility, since different types of processing (e.g.baseline correction, different values and types of the high-pass filter) can be chosen for the real and imaginary part separately, if necessary.

Effect of the shape of the time filter
For the sake of simplicity and to showcase the general applicability of the approach, only a Heaviside time-domain filter was used for the results presented in the main part of this work.However, other types of commonly used filters can be applied. .For example, a 1 st -order Butterworth filter can significantly decrease the fringes next to absorption lines, since it dampens the roll-off in the filtered spectra (see Figure S3b).On the other hand, this also means that in the TD the cut-off is not sharp, and more noise from the excitation (which is centered around 0 fs) might be picked up.